Why did my iphone ask for my macbook air password?

To allow recovery of end-to-end encrypted content (Keychain, Health data, HomeKit, etc.) your device passwords are used.

When your phone prompted for your MacBook Air password, it needed that password to gain trusted access to those items in iCloud. This is normal and you were correct to enter the password (to the same extent you would have been correct to enter your iCloud password in the same context).

The alternative is reduced account security or the inability to recover those items if you forget your main Apple ID password.

Just because you have Keychain off does not mean that your devices to not get access to this trusted data store. They are still authorized, they simply will not when those checkboxes are disabled. The alternative would have been resetting those parts of the iCloud data store (in most cases they would be automatically refilled from on-device data).

To allow/continue use of iCloud Keychain.

Set up iCloud Keychain